Mr. A. Cayley on Caustics. 9'B 



This fact naturally suggests the possibihty of correcting the defect 

 of the refracting stereoscope ; for if the images of the camera were 

 taken by semi-lenses, the bend resulting from this mode of operatmg 

 might be corrected by the bend of the stereoscope, care bemg taken 

 to turn the thin edge of the semi-lenses of the two cameras m the 

 direction which will produce a bending contrary to that ot the semi- 

 lenses of the stereoscope. 



Having shown how the lateral proportional distances ot any two 

 correspondent points of the two stereoscopic pictures are the indices 

 of their perspective distances, if we were, while looking in the stereo- 

 scope, to produce a change in those proportional lateral distances by 

 sliding horizontallv in a contrary direction, two pairs of superposed 

 glass photographic pictures, the objects would appear to move, not in 

 the horizontal lateral direction of that change which they naturally 

 have, but in a straight hne forward and backward, as it the object 

 was approaching or receding. ,, ,,, i- ^ 



But the most curious effect of that motion would be, that the objects 

 would appear increasing in size while they were receding, and diminish- 

 ing while approaching, which we know is contrary to the rule ot 

 perspective. This is another illusion entirely physiological, and the 

 cause of which may be thus explained ; while the object appears 

 moving forward and backward it remains always the same size, but 

 as we expect when it moves forward that it should increase in size, 

 and when it moves backward that it should decrease, and as it does 

 not, we feel that it is diminishing when approaching and increasing 

 when receding. 



" A Memoir upon Caustics." By Arthur Cayley, Esq., F.R.S. 

 The principal object of this memoir, which contams little or nothing 

 that can be considered new in principle, is to collect together the 

 principal results relating to caustics in piano, the reflecting or refract- 

 ing curve being a right hne or a circle, and to discuss with more 

 care than appears to have been hitherto bestowed upon the subject, 

 some of the more remarkable cases. The memoir contains m parti- 

 cular researches relating to the caustic by refraction of a circle for 

 parallel rays, the caustic by reflexion of a circle for rays proceeding 

 from a point, and the caustic by refraction of a circle for rays pro- 

 ceeding from a point ; the result in the last case is not worked out, 

 but it!s shown how the equation in rectangular coordinates is to be 

 obtained by equating to zero the discriminant of a rational and inte- 

 gral function of the sixth degree. The memoir treats also of the 

 Secondary caustic or orthogonal trajectory of the reflected or refracted 

 rays in the generul case of a reflecting or refracting circle and rays 

 proceeding from a point ; the curve in question, or rather « secondary 

 caustic, isT as is well known, the Oval of Descartes or 'Cartesian: 

 the equation is discussed by a method which gives rise to some forms 

 of the curve which appear to have escaped the notice of geometers 

 By considering the caustic as the evolute of the secondary caustic, it 

 is shown that the caustic in the general case of a reflecting or refract- 

 m>r circle and rays proceeding from a point is a curve of the sixth 

 £s only. The ^olicluding fart of the memoir treats of the curve 



